Problem: Solve for $x$ : $10\sqrt{x} + 5 = 7\sqrt{x} + 9$
Solution: Subtract $7\sqrt{x}$ from both sides: $(10\sqrt{x} + 5) - 7\sqrt{x} = (7\sqrt{x} + 9) - 7\sqrt{x}$ $3\sqrt{x} + 5 = 9$ Subtract $5$ from both sides: $(3\sqrt{x} + 5) - 5 = 9 - 5$ $3\sqrt{x} = 4$ Divide both sides by $3$ $\frac{3\sqrt{x}}{3} = \frac{4}{3}$ Simplify. $\sqrt{x} = \dfrac{4}{3}$ Square both sides. $\sqrt{x} \cdot \sqrt{x} = \dfrac{4}{3} \cdot \dfrac{4}{3}$ $x = \dfrac{16}{9}$